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Question: There are how many 4-digit even numbers if the first digit cannot be a zero?
- 3600
- 3645
- 4500
- 4999
- 5000
Answer
Approach Solution (1)
The first digit of the 4-digit number can be any of 9 digits (1 through 9, inclusive)
The second digit can be any of 10 digits (0 through 9, inclusive), and the same is true for the third digit
The fourth digit must be even, and there are 5 even digits (0, 2, 4, 6, or 8)
Thus, the number of 4-digit even numbers is 9 x 10 x 10 x 5 = 4500
The second digit can be any of 10 digits (0 through 9, inclusive), and the same is true for the third digit
The fourth digit must be even, and there are 5 even digits (0, 2, 4, 6, or 8)
Thus, the number of 4-digit even numbers is 9 x 10 x 10 x 5 = 4500
Correct option: C
Approach Solution (2)
These are four digit even numbers, so the first digit can be 1 to 9, and the unit digit can be 2,4,6,8, or 0..
Any number of repetitions can be done
Units digit = any of five even digits = 0,2,4,6,8
At tens and hundreds position any of the ten digits can be placed
At thousands places, any of the 10 except 0 can be placed
Any number of repetitions can be done
Units digit = any of five even digits = 0,2,4,6,8
At tens and hundreds position any of the ten digits can be placed
At thousands places, any of the 10 except 0 can be placed
Correct option: C
Approach Solution (3)
Different ways without any restriction =10 * 10 * 10 * 10 = 10,000
Out of these ways in which first digit is 0 = 1 * 10 * 10 * 10 = 1000
Remaining = 10000 - 1000 = 9000
Half of 9000 will be even and other half odd
So, even = 9000 / 2 = 4500
Out of these ways in which first digit is 0 = 1 * 10 * 10 * 10 = 1000
Remaining = 10000 - 1000 = 9000
Half of 9000 will be even and other half odd
So, even = 9000 / 2 = 4500
Correct option: C
“There are how many 4-digit even numbers if the first digit cannot be a zero?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.
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